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Simplifying 0.25(20z + 3) = 0.75(8z + 1) Reorder the terms: 0.25(3 + 20z) = 0.75(8z + 1) (3 * 0.25 + 20z * 0.25) = 0.75(8z + 1) (0.75 + 5z) = 0.75(8z + 1) Reorder the terms: 0.75 + 5z = 0.75(1 + 8z) 0.75 + 5z = (1 * 0.75 + 8z * 0.75) 0.75 + 5z = (0.75 + 6z) Add '-0.75' to each side of the equation. 0.75 + -0.75 + 5z = 0.75 + -0.75 + 6z Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 5z = 0.75 + -0.75 + 6z 5z = 0.75 + -0.75 + 6z Combine like terms: 0.75 + -0.75 = 0.00 5z = 0.00 + 6z 5z = 6z Solving 5z = 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 5z + -6z = 6z + -6z Combine like terms: 5z + -6z = -1z -1z = 6z + -6z Combine like terms: 6z + -6z = 0 -1z = 0 Divide each side by '-1'. z = 0 Simplifying z = 0
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